As you enter your senior year, graduate roles are the priority. Stress will speed as the year proceeds so complete most/all of the application related tasks as soon as possible. Some graduate employers, including the large accountancy firms and banks, open inquiries for the graduate training schemes as early as summer i.e. June/July. You should start checking out graduate jobs from the summer before you begin your final year. Ideally, you should have completed all of your applications by November.
In October or November, employers will also be on campus, giving you a chance to meet them and ask questions. Check University Careers services events calendar to find out about when employers are on campus. It will often take a few applications to learn how to do them well, and once you have mastered it, you can do them fast.